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Keywords:
neutral differential equation; oscillatory (nonoscillatory) solution; quasi derivatives
neutral differential equation; oscillatory (nonoscillatory) solution; quasi derivatives
Summary:
The authors study the n-th order nonlinear neutral differential equations with the quasi – derivatives $L_n[x(t)+(-1)^r P(t) x(g(t))]+\delta Q(t) f(x(h(t))) = 0,$ where $\ n \ge 2,\ r \in \lbrace 1,2\rbrace ,\ $ and $ \delta = \pm 1.$ There are given sufficient conditions for solutions to be either oscillatory or they converge to zero.
References:
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[2] Jaroš, J., Kusano, T.: Oscillation properties of first order nonlinear functional differential equations of neutral type. Diff. and Int. Equat. (1991), 425-436. MR 1081192
[3] Marušiak, P.: Oscillatory properties of functional differential systems of neutral type. Czech. Math. J. 43 (1993), 649-662. MR 1258427
[4] Šeda, V.: Nonoscillatory solutions of differential equations with deviating argument. Czech. Math. J. 36 (111) (1986), 93-107. MR 0822871
[5] Zafer, A., Dahiya, R. S.: Oscillation of bounded solutions of neutral differential equations. Appl. Math. Lett. 2 (1993), 43-46. MR 1347773
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